Illegal immigration has emerged as a dominant campaign issue for Republicans seeking the presidential nomination, with candidates competing to appear the most conservative. But Latino political organizations warn that the harsh stance on immigrants is alienating Latino voters crucial to a Republican victory in the general election. Leta Hong Fincher has more.

Mitt Romney attacked Senator John McCain in the run-up to the New Hampshire primary for backing legislation to offer illegal immigrants a path to U.S. citizenship.

"In my opinion, that's a form of amnesty. In my opinion, that is wrong, that will only encourage more illegal immigration. It's time to stop illegal immigration," he said.

Immigration dominated their exchange during the Republican presidential debate Saturday, January 5, on the ABC News TV network:

Romney: "They should not be given a special right to stay here." McCain: "There is no special right associated with my plan. I said they should not be in any way rewarded for illegal behavior." Romney: "Are they sent home?" McCain: "They have to get in line..." Romney: "Are they sent home?" McCain: "... behind everybody else." Romney: "Are they sent home?"McCain: "Some of them are, some of them are not."

Political analysts say the Republican Party has become more conservative on immigration since President Bush's failed effort over the past two years to promote immigration reform. The legislation would bolster security and offer 12 million illegal immigrants in the United States a path to citizenship.

Romney would cut federal funding to cities that refuse to comply with immigration laws. Former Arkansas governor Mike Huckabee would give illegal immigrants 120 days to register with federal authorities and leave the country.

McCain has come under attack from his rivals for wanting to give illegal immigrants a path to citizenship. Even so, he supports a vast increase in U.S. border surveillance.

But how many voters across the United States consider illegal immigration their top issue in choosing the next president? Not many, says Scott Keeter, who directs survey research at the Pew Research Center in Washington. "Immigration has consistently been near the bottom of the list in terms of the percentage [of voters] saying that it's very important."

Still, Keeter says that taking a tough stance on illegal immigration could energize a minority of conservative Republican voters to turn out on election day. "There is this intense minority that opposes [illegal immigration], wants to see all illegal immigrants leave the country, and their voting power may be greater than their numbers simply because they feel so strongly about the issue," he explained.

Latino political organizations warn that the Republican strategy could backfire by alienating Latino voters.

Cecilia Muñoz supervises public policy at the National Council of La Raza, the largest Latino advocacy group in the country. She said the candidates are mistaken if they think the issue is a small one. "These candidates think that they can draw a box around illegal immigrants and say 'we just mean them, and so Latinos who are voters, who are U.S. citizens shouldn't be a problem;' but they're mistaken because they're really attacking the entire community," said Muñoz.

Muñoz notes Latinos are the fastest growing sector of the U.S. electorate, and that at least nine million Latinos are expected to vote in November's general election.

"One wonders when one of these candidates wins the nomination for their party, how they're going to turn around and try to entice the Latino vote after they've been essentially insulting this community throughout the primary season," she said. "I don't think it can be done."

Muñoz adds that President Bush won about 40 percent of the Latino vote during his reelection bid in 2004. She and other pollsters argue that the eventual Republican nominee in 2008 will not gain anywhere near that level of Latino support.